Dwivedi Shubham, Herman Jonathan, Jeffrey Lisa C. Hamiltonian Group Actions and Equivariant Cohomology 9783030272265

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Автор: Dwivedi Shubham, Herman Jonathan, Jeffrey Lisa C.
Название: Hamiltonian Group Actions and Equivariant Cohomology
ISBN: 9783030272265
Издательство: Springer
Классификация:

Геометрия

Топология

Системы и технологии визуализации

ISBN-10: 3030272265
Обложка/Формат: Paperback
Страницы: 132
Вес: 0.23 кг.
Дата издания: 17.11.2019
Серия: Springerbriefs in mathematics
Язык: English
Издание: 1st ed. 2019
Иллюстрации: 1 illustrations, color; 2 illustrations, black and white; xi, 132 p. 3 illus., 1 illus. in color.
Размер: 234 x 156 x 8
Читательская аудитория: Professional & vocational
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: This monograph could be used for a graduate course on symplectic geometry as well as for independent study.The monograph starts with an introduction of symplectic vector spaces, followed by symplectic manifolds and then Hamiltonian group actions and the Darboux theorem. After discussing moment maps and orbits of the coadjoint action, symplectic quotients are studied. The convexity theorem and toric manifolds come next and we give a comprehensive treatment of Equivariant cohomology. The monograph also contains detailed treatment of the Duistermaat-Heckman Theorem, geometric quantization, and flat connections on 2-manifolds. Finally, there is an appendix which provides background material on Lie groups. A course on differential topology is an essential prerequisite for this course. Some of the later material will be more accessible to readers who have had a basic course on algebraic topology. For some of the later chapters, it would be helpful to have some background on representation theory and complex geometry.
Дополнительное описание: Symplectic vector spaces.- Hamiltonian group actions.- The Darboux-Weinstein Theorem.- Elementary properties of moment maps.- The symplectic structure on coadjoint orbits.- Symplectic Reduction.- Convexity.- Toric Manifolds.- Equivariant Cohomology.- The

Hamiltonian Group Actions and Equivariant Cohomology, Dwivedi Shubham, Herman Jonathan, Jeffrey Lisa C.